Allocating Bandwidth in a Resilient Packet Ring Network by PI Controller

ABSTRACT

Implementations and techniques for allocating bandwidth in a resilient packet ring network by a PI-type controller are generally disclosed.

CROSS-REFERENCES TO OTHER APPLICATIONS

The present application is related to U.S. application Ser. No. ______filed ______, entitled ALLOCATING BANDWIDTH IN A RESILIENT PACKET RINGNETWORK BY P CONTROLLER by Fahd Alharbi and Nirwan Ansari.

BACKGROUND

Resilient Packet Ring (RPR) networks are often utilized as a metrotechnology due at least in part on protection and fault toleranceproperties. However, some metro networking technologies exhibit severallimitations. For example, in a Synchronous Optical Networking-type(SONET) ring, individual nodes may be granted with a minimum fair share;however, it may not be possible to reclaim the unused bandwidth.Moreover, a percentage of the potentially available bandwidth may bereserved for protection, thus potentially resulting in poor utilization.On the other hand, a Gigabit Ethernet-type ring may result in fullstatistical multiplexing at the expense of fairness. RPR networks may beutilized to mitigate the respective underutilization and unfairnessproblems associated with the current SONET-type ring and Ethernet-typering technologies.

BRIEF DESCRIPTION OF THE DRAWINGS

Subject matter is particularly pointed out and distinctly claimed in theconcluding portion of the specification. The foregoing and otherfeatures of the present disclosure will become more fully apparent fromthe following description and appended claims, taken in conjunction withthe accompanying drawings. Understanding that these drawings depict onlyseveral embodiments in accordance with the disclosure and are,therefore, not to be considered limiting of its scope, the disclosurewill be described with additional specificity and detail through use ofthe accompanying drawings.

FIG. 1 illustrates a diagram of an example RPR ring;

FIG. 2 illustrates a block diagram of a given node of an example RPRring;

FIG. 3 illustrates a flow chart illustrating an example process forallocating bandwidth in a resilient packet ring network;

FIG. 4 illustrates an example control process for allocating bandwidthin a resilient packet ring network;

FIG. 5 illustrates a diagram of an example unbalanced traffic scenario;

FIG. 6 illustrates a diagram of an example unbalanced traffic scenario;

FIG. 7 illustrates a chart of throughput over time under an exampleunbalanced traffic scenario;

FIG. 8 illustrates a chart of throughput over time under an exampleunbalanced traffic scenario;

FIG. 9 illustrates a chart of transit queue buffer occupancy over timeunder an example unbalanced traffic scenario;

FIG. 10 illustrates a chart of end-to-end delay over time under anexample unbalanced traffic scenario;

FIG. 11 illustrates an example computer program product; and

FIG. 12 is a block diagram illustrating an example computing device, allarranged in accordance with the present disclosure.

DETAILED DESCRIPTION

The following description sets forth various examples along withspecific details to provide a thorough understanding of claimed subjectmatter. It will be understood by those skilled in the art, however, thatclaimed subject matter may be practiced without some or more of thespecific details disclosed herein. Further, in some circumstances,well-known methods, procedures, systems, components and/or circuits havenot been described in detail in order to avoid unnecessarily obscuringclaimed subject matter. In the following detailed description, referenceis made to the accompanying drawings, which form a part hereof. In thedrawings, similar symbols typically identify similar components, unlesscontext dictates otherwise. The illustrative embodiments described inthe detailed description, drawings, and claims are not meant to belimiting. Other embodiments may be utilized, and other changes may bemade, without departing from the spirit or scope of the subject matterpresented here. It will be readily understood that the aspects of thepresent disclosure, as generally described herein, and illustrated inthe Figures, can be arranged, substituted, combined, and designed in awide variety of different configurations, all of which are explicitlycontemplated and make part of this disclosure.

This disclosure is drawn, inter alia, to methods, apparatus, systemsand/or computer program products related to allocating bandwidth in aresilient packet ring (RPR) network by a proportional-integral (PI-type)controller.

RPR networks may be utilized as a high-speed backbone technology formetropolitan area networks. For example, RPR networks may be introducedto mitigate underutilization and unfairness problems associated withSONET-type ring and Ethernet-type ring technologies, respectively. Someperformance objectives of RPR may include achieving high bandwidthutilization, optimum spatial reuse on the dual rings of an RPR, and/orfairness.

One challenge may be to design an algorithm that can react dynamicallyto the traffics in achieving such performance objectives. Aggressivemode (RPR-AM) and conservative mode (RPR-CM) RPR fairness algorithms maybe comparatively simple processes, but may pose some limitations. Forexample, one such limitation may be that the amount of band-widthallocated by RPR-CM and/or RPR-AM may oscillate under unbalanced trafficscenarios. Such unbalanced traffic scenarios will be described ingreater detail below with respect to examples illustrated in FIGS. 5 and6. These oscillations may be a barrier to achieving spatial reuse and/orhigh bandwidth utilization. Moreover, the performance of RPR-CM and/orRPR-AM may be sensitive to algorithm parameter settings. Accordingly,methods, apparatus, systems and/or computer program products related toallocating bandwidth in a RPR network via a proportional-integral(PI-type) controller will be described below to address limitations ofRPR-CM and/or RPR-AM fairness algorithms.

FIG. 1 illustrates a diagram of an example RPR network 100 in accordancewith one or more example implementations. RPR network 100 may includetwo rotating ringlets. For example, one such ringlet may be referred toas the inner ringlet 102, and the other such ringlet may be referred toas the outer ringlet 104. Inner and outer ringlets 102, 104 may traversetwo or more nodes. For example, inner and outer ringlets 102, 104 maytraverse nodes 106A, 106B, 106C, 106D, 106E, and 106F. A portion ofinner ringlet 102 or outer ringlet 104 that operably associates twoadjacent nodes 106A, 106B together may be referred to as a link 108.Accordingly, inner ringlet 102 and/or outer ringlet 104 may includeseveral links 108 operably associated between two or more nodes 106A,106B, 106C, 106D, 106E, and 106F. In operation, information may enterRPR network 100 at a given upstream node, such as node 106A, and maypass along inner ringlet 102 or outer ringlet 104 via one or more links108 to a downstream destination node, such as node 106B. In such a case,when such information reaches a downstream destination node, such asnode 106B, such information may then pass out of RPR network 100.

FIG. 2 illustrates a block diagram of a given node 106B of an exampleRPR network 100 (FIG. 1) arranged in accordance with at least someembodiments of the present disclosure. Node 106B may include hardware,software and/or any combination thereof capable of performing thefunctions of ingress data measurements, congestion, and bandwidthallocation. For example, node 106B may include one or more ratecontrollers 210, one or more local buffers 212, a primary transit queue(PTQ) buffer 214, a secondary transit queue (STQ) buffer 216, a checker218, a scheduler 220, and/or a PI-type controller 222. These functionalunits may operate to perform a flow control in the RPR network 100 (FIG.1). Such flow control may allow a congested node 106B to send a fairnessmessage (derived according to measurements made at node 106B) to one ormore upstream nodes 106A, etc. (FIG. 1). Such a fairness message mayresult in one or more upstream nodes 106A, etc. (FIG. 1) throttlingingress information rates in order to reduce and/or eliminate a state ofcongestion at congested node 106B and apply fairness among participatingnodes 106A, etc. (FIG. 1).

Node 106B may utilize one or more rate controllers 210 to throttlestation traffic 230 entering RPR network 100 (FIG. 1). For example, ratecontrollers 210 may throttle station traffic 230 on a per-destinationbasis to support virtual destination queuing and/or avoid head-of-lineblocking (HOL). As used herein, HOL blocking may refer to situationswhere a head-of-line packet of a certain buffer cannot be switched to adestination because of congestion along the path from source todestination, potentially resulting in the rest of the packets in thatbuffer being blocked by that head-of-line packet, even if there is nocongestion along the path from the source to their destinations.Additionally or alternatively, rate controllers 210 may permit stationtraffic 230 to be delivered to local buffers 212. Local buffers 212 maydefine several service classes of user traffic. For example, localbuffers 212 may define Class A user traffic with guaranteed rate andjitter; Class B user traffic with a committed information rate (CIR) andbounded delay and jitter; and/or Class C user traffic as best efforttraffic.

Checker 218 may receive inlet traffic 232 from ringlet (not shown) intonode 106B. Checker 218 may shunt egress traffic 234 out of node 106B.Additionally or alternatively, checker 218 may forward transit traffic236 through to PTQ buffer 214 and/or STQ buffer 216

Scheduler 220 may coordinate the flow of information out from PTQ buffer214, STQ buffer 216, and/or local buffers 212. For example, scheduler220 may selectively permit outlet traffic 238 from PTQ buffer 214, STQbuffer 216, and/or local buffers 212 to exit node 106B to continue alongRPR network 100 (FIG. 1). For example, 220 may selectively permit outlettraffic 238 from PTQ buffer 214 first. In cases where PTQ buffer 214 isempty, STQ buffer 216 may have priority over the station traffic fromlocal buffers 212. For example, STQ buffer 216 may have priority overthe station traffic from local buffers 212 in cases where the STQ queuelength exceeds an STQ threshold; otherwise, the station traffic 230 maybe served. In such a case, station traffic 230 may be divided into oneor more classes of importance, such as Class A, Class B, Class C, and/orthe like. For example station traffic 230 may be served in the followingorder: Class A traffic, then Class B traffic. In cases where node 106Bhas no Class A or B traffic, then Class C traffic may be served.

PI-type controller 222 may receive traffic measurements, includingtransit queue length 240. For example, PI-type controller 222 mayreceive traffic measurements regarding a transit queue length 240associated with STQ buffer 216. Based at least in part on such trafficmeasurements, PI-type controller 222 may apply a fairness algorithm todetermine a fair rate F(n). Such a determined a fair rate may beutilized to allocate bandwidth in RPR network 100 (FIG. 1). For example,such a determined a fair rate may be sent to upstream nodes 106A, etc.(FIG. 1) in the form of a control message 242. Such upstream nodes 106A,etc. (FIG. 1) that receive control message 242 may use the controlmessage information and/or local information to throttle ratesaccordingly.

FIG. 3 illustrates a flow chart illustrating an example process 300 forallocating bandwidth in a resilient packet ring network, in accordancewith at least some embodiments of the present disclosure. Process 300,and other processes described herein, set forth various functionalblocks or actions that may be described as processing steps, functionaloperations, events and/or acts, etc., and that may be performed byhardware, software, and/or firmware. Those skilled in the art in lightof the present disclosure will recognize that numerous alternatives tothe functional blocks shown in FIG. 3 may be practiced in variousimplementations. For example, although process 300, as shown in FIG. 3,comprises one particular order of blocks or actions, the order in whichthese blocks or actions are presented does not necessarily limit claimedsubject matter to any particular order. Likewise, intervening actionsnot shown in FIG. 3 and/or additional actions not shown in FIG. 3 may beemployed and/or some of the actions shown in FIG. 3 may be eliminated,without departing from the scope of claimed subject matter.

As illustrated, process 300 may be implemented to allocate bandwidth ina resilient packet ring network. Processing begins at action 302, whereat the end of a given sampling time T, a PI-type controller 222 (FIG. 2)at downstream node 106B may sample the current transit queue length. Forexample, downstream node 106B may sample the current transit queuelength of STQ buffer 216 (FIG. 2). As used herein, the term “samplingtime T” may refer to a sampling time between a determination of acurrent fair rate F(n) and a determination of a prior fair rate F(n−1).Processing continues from action 302 to 304 where the transit queuelength may be compared with a target queue length. For example, PI-typecontroller 222 (FIG. 2) at downstream node 106B may compare the currenttransit queue length of STQ buffer 216 (FIG. 2) with a previouslyspecified target queue length.

Continuing to action 306, a fair rate may be determined. For example,PI-type controller 222 (FIG. 2) at downstream node 106B may determine afair rate based at least in part on the comparison of the currenttransit queue length of STQ buffer 216 (FIG. 2) to the previouslyspecified target queue length. In one implementation, such a fair ratemay be determined so as to facilitate an allocated bandwidth in RPRnetwork 100 via PI-type controller 222 (FIG. 2) associated with at leastone node of RPR network 100, such as downstream node 106B, for example.

Continuing to action 308, such a determined fair rate may be forwardedto one or more upstream nodes 106A. For example, downstream node 106Bmay forward a fair rate to one or more upstream nodes 106A on anopposite ringlet 102 (FIG. 1). Accordingly, individual upstream nodes106A may be made aware of the supported fair rates at downstream node106B. Additionally or alternatively, similar fair rates may bedetermined broadcast from other nodes (such as nodes 106C, etc.) in RPRnetwork 100. Accordingly, individual nodes 106A, 106B, etc. in RPRnetwork 100 may be made aware of the supported fair rates at downstreamnode 106B, and/or the supported fair rates at individual nodes 106A,106B, etc. in RPR network 100.

Continuing to action 310, downstream node 106A may adjust its forwardingrate. For example, upstream node 106A may adjust its forwarding ratebased at least in part on the fair rate received from downstream node106B. As will be discussed in greater detail below, the operation ofprocedure 300 may result in stabilizing the transit queue lengths at atarget queue length, as is illustrated at action 312. For example, oneor more transit queue lengths may be stabilized at a target queue lengthunder unbalanced traffic scenarios, based at least in part on anallocated bandwidth, discussed above with respect to action 306. In oneimplementation, at action 312, downstream node 106A may repeat one ormore of actions 302-308 to stabilize one or more transit queue lengthsof STQ buffer 216 (FIG. 2) at a target queue length. Additionally oralternatively, similar actions may be taken at other nodes (such asnodes 106C, etc.) in RPR network 100. Accordingly, individual nodes106C, 106D, etc. (FIG. 1) in RPR network 100 may also stabilize the oneor more transit queue lengths of STQ buffers 216 (FIG. 2) respectivelyassociated with the individual nodes 106C, 106D, etc. (FIG. 1) in RPRnetwork 100. Additionally or alternatively, such stabilization of one ormore transit queue lengths may be achievable under unbalanced trafficscenarios.

FIG. 4 illustrates an example control process 400 for allocatingbandwidth in a resilient packet ring network, in accordance with atleast some embodiments of the present disclosure. Process 400, and otherprocesses described herein, set forth various functional blocks oractions that may be described as processing steps, functionaloperations, events and/or acts, etc., and that may be performed byhardware, software, and/or firmware. Those skilled in the art in lightof the present disclosure will recognize that numerous alternatives tothe functional blocks shown in FIG. 4 may be practiced in variousimplementations. For example, although process 400, as shown in FIG. 4,comprises one particular order of blocks or actions, the order in whichthese blocks or actions are presented does not necessarily limit claimedsubject matter to any particular order. Likewise, intervening actionsnot shown in FIG. 4 and/or additional actions not shown in FIG. 4 may beemployed and/or some of the actions shown in FIG. 4 may be eliminated,without departing from the scope of claimed subject matter.

As illustrated, control process 400 may be implemented to allocatebandwidth in a resilient packet ring network. At block 401, a comparisonof the transit queue length Q(s) 402 and the target queue length Q_(T)404 may be made. For example, an error E(s) 406 may be determined toquantify such a comparison of the transit queue length Q(s) 402 and thetarget queue length Q_(T) 404. In one implementation, error E(s) 406 maybe determined based at least in part on the following equation:

E(s)=Q _(T)(s)−Q(s)   (eq. 1)

Processing continues from block 401 to block 408, where a fair rate F(s)410 may be determined based at least in part on the comparison of thetransit queue length Q(s) 402 and the target queue length Q_(T) 404. Forexample, error E(s) 406 may be modified based at least in part on aproportional gain k_(p) and/or an integral gain integral gain k_(I) toresult in fair rate F(s) 410, as illustrated at block 408. In oneimplementation, fair rate F(s) 410 may be determined based at least inpart on the following equation:

$\begin{matrix}{{F(s)} = {\left( {k_{p} + \frac{k_{1}}{s}} \right){E(s)}}} & \left( {{eq}.\mspace{14mu} 2} \right)\end{matrix}$

Processing continues from block 408 to block 412, where an updatedtransit queue length Q(s) 402 may be determined. For example, updatedtransit queue length Q(s) 402 may be determined based at least in parton fair rate F(s) 410. In one implementation, fair rate F(s) 410 may bemodified based at least in part on the following equation to determineupdated transit queue length Q(s) 402:

$\begin{matrix}{{Q(s)} = {\frac{\sum\limits_{i = 1}^{N}{w_{i}^{{- s}\; \tau_{i}}}}{s}{F(s)}}} & \left( {{eq}.\mspace{14mu} 3} \right)\end{matrix}$

Block 412 of the control process 400 is illustrated in FIG. 4 where Wmay represent a sum of weights associated with various nodes of a RPRnetwork as follows:

$\begin{matrix}{W = {\sum\limits_{i = 1}^{N}w_{i}}} & \left( {{eq}.\mspace{14mu} 4} \right)\end{matrix}$

Additionally, τ_(i) may represent the round trip delay between abottleneck link 108 (FIG. 1) and a source node i of a RPR network. Sucha round trip delay τ_(i) may represent an amount of time betweeninitiation of communications at downstream node 106B (FIG. 1) andreceipt at upstream node 106A (FIG. 1), represented by backward delayτhd i^(b), and may represent an amount of time between initiation ofcommunications at upstream node 106A (FIG. 1) and receipt at downstreamnode 106B (FIG. 1), represented by forward delay τ_(i) ^(f). Forexample, round trip delay τ_(i) may be calculated as τ_(i)=τ_(i)^(b)+τ_(i) ^(f), where τ_(i) ^(b) may represent a backward delay from abottlenecked link 108 (FIG. 1) to a source node i, and where τ_(i) ^(f)may represent a forward delay from source node i to bottlenecked link108 (FIG. 1). In one implementation, τ may represent an upper bound ofsuch a round trip delay τ_(i).

More particularly, control process 400 may be better understood withreference to the following discussion regarding the formation of controlprocess 400. At a bottleneck link 108 (FIG. 1) associated with adownstream node 106B (FIG. 1), a rate of change of a transit queuelength 402 may be written as follows:

$\begin{matrix}{{q_{l}^{\prime}(t)} = {{\sum\limits_{i = 1}^{N}{r_{i}\left( {t - \tau_{i}^{f}} \right)}} - C}} & \left( {{eq}.\mspace{14mu} 5} \right)\end{matrix}$

In such a case, r_(i) may represent a transmitting rate of source nodei, such as upstream node 106A (FIG. 1), τ_(i) ^(f) may represent theforward delay from source node i to the bottlenecked link 108 (FIG. 1),t may represent time, N may represent the number of source nodes, and Cmay represent the available bandwidth of downstream node 106B (FIG. 1)associated with bottleneck link 108 (FIG. 1). For example, a rate ofchange of a transit queue length 402 may be proportional to traffictransmitted from upstream source nodes i through bottleneck link 108(FIG. 1) associated with downstream node 106B (FIG. 1), when taking intoconsideration available bandwidth C and forward delay τ_(i) ^(f).

One or more of source nodes i, such as upstream node 106A (FIG. 1), maytransmit information at rate according to a received fair rate f fromthe bottlenecked link 108 (FIG. 1) associated with a downstream node106B (FIG. 1) as follows:

r _(i)(t)=w _(i) f(t−τ _(i) ^(b))   (eq. 6)

In such a case, w_(i) may represent a weight less than or equal to one,and τ_(i) ^(b) may represent the backward delay from bottlenecked link108 (FIG. 1) associated with a downstream node 106B (FIG. 1) to sourcenode i, such as upstream node 106A (FIG. 1).

A fair rate f(t) for bottlenecked link 108 (FIG. 1) associated with adownstream node 106B (FIG. 1) may be represented as follows:

f(t)=k _(p) e(t)+₁ ∫e(t)   (eq. 7)

In such a case, k_(p) may represent a proportional gain for a PI-typecontroller, k_(I) may represent an integral gain for a PI-typecontroller, and e(t)=q_(T)−q(t) may represent a difference between atransit queue length q(t) and a target queue length q_(T).

RPR network 100 (FIG. 1) may be represented as closed-loop system thatmay include an equilibrium point at which

${{\lim\limits_{t\rightarrow\; \infty}{q^{\prime}(t)}} = 0},{{\lim\limits_{t\rightarrow\; \infty}{q(t)}} = q_{T}},{{{and}\mspace{14mu} {\lim\limits_{t\rightarrow\; \infty}{f(t)}}} = {f^{*}.}}$

In such a case, f* may represent an optimal fair rate. Thus, (eq. 5), atthe equilibrium point can be written as follows:

$\begin{matrix}{{\sum\limits_{i = 1}^{N}r_{i}^{*}} = C} & \left( {{eq}.\mspace{14mu} 8} \right)\end{matrix}$

In such a case, r* may represent an optimal rate that individual sourcenodes i, such as upstream node 106A (FIG. 1), may transmit throughbottlenecked link 108 (FIG. 1) associated with a downstream node 106B(FIG. 1).

Using (eq. 8) and (eq. 6), the following may be obtained:

$\begin{matrix}{{\sum\limits_{i = 1}^{N}{w_{i}f^{*}}} = C} & \left( {{eq}.\mspace{14mu} 9} \right)\end{matrix}$

In such a case, (eq. 9) may establish that the PI-type controller mayachieve the following weighted max-min fair rates:

$\begin{matrix}{f^{*} = \frac{C}{\sum\limits_{i = 1}^{N}w_{i}}} & \left( {{eq}.\mspace{14mu} 10} \right)\end{matrix}$

In addition to the weighted max-min fair rates of (eq. 10) describedabove, stability conditions for controller gains, including proportionalgain k_(p) and/or integral gain k_(I) for PI-type controller may befound. Using (eq. 5) and (eq. 6), the following may be obtained:

$\begin{matrix}{{q_{l}^{''}(t)} = {\sum\limits_{i = 1}^{N}\; {w_{i}{f^{\prime}\left( {t - \tau_{i}} \right)}}}} & \left( {{eq}.\mspace{14mu} 11} \right)\end{matrix}$

In such a case, τ_(i)=τ_(i) ^(b)+τ_(i) ^(f) may represent a round triptime between source node i, such as upstream node 106A (FIG. 1), andbottlenecked link 108 (FIG. 1) associated with a downstream node 106B(FIG. 1), for example.

By taking the Laplace transform of (eq. 8) and (eq. 11), the following(eq. 2) and/or (eq. 3), discussed above, may be obtained:

$\begin{matrix}{{{F(s)} = {\left( {k_{p} + \frac{k_{I}}{s}} \right){E(s)}}},{and}} & \left( {{eq}.\mspace{14mu} 2} \right) \\{{Q(s)} = {\frac{\sum\limits_{i = 1}^{N}\; {w_{i}^{{- s}\; \tau_{i}}}}{s}{F(s)}}} & \left( {{eq}.\mspace{14mu} 3} \right)\end{matrix}$

For simplicity, it may be assumed that round trip delay τ_(i)=τ, ∀ i ∈ N. In such a case, τ may represent an upper bound of round trip delayτ_(i). Accordingly, control process 400 may be formulated based at leastin part on (eq. 2), (eq. 3), and/or (eq. 1).

Control process 400 illustrated in FIG. 4, may be represented at leastin part by a characteristic equation in the Laplace domain as follows:

$\begin{matrix}{{1 + \frac{\left( {k_{p} + \frac{k_{I}}{s}} \right)W\; ^{{- s}\; \tau}}{s}} = 0} & \left( {{eq}.\mspace{14mu} 12} \right)\end{matrix}$

A first order Taylor series may be utilized to approximate theexponential function utilized at block 412 of control process 400, e.g.,e^(−sτ)=1−sτ. Thus, based at least in part on a first order Taylorseries, (eq. 12) may be rewritten as follows:

(1−Wk _(p)τ)s ²+(Wk _(p) −Wk _(I)τ)s+Wk _(I)=0   (eq. 13)

The characteristic equation of (eq. 13) is in the form of a second orderquadratic equation as follow:

a ₀ s+a ₁ s+a ₂=   (eq. 14)

To compute controller gains, including proportional gain k_(p) and/orintegral gain k_(I) for PI-type controller, a Routh array may beconstructed based at least in part on (eq. 13) in the form of a secondorder quadratic equation (eq. 14) as follows in Table 1:

TABLE 1 Row 1 (1 − Wk_(p)τ) Wk_(I) 2 (Wk_(p) − Wk_(I)τ) 0 3 Wk_(I)One condition for stability may be that the elements in the first columnof Table 1 must be positive. After some algebraic manipulation, thefollowing conditions under which a closed-loop system may be stable maybe obtained, based at least in part on the stability conditions fromTable 1, above:

$\begin{matrix}{{0 < k_{p} < \frac{1}{W\; \tau}},{and}} & \left( {{eq}.\mspace{14mu} 15} \right) \\{0 < k_{I} < {\frac{k_{P}}{\tau}.}} & \left( {{eq}.\mspace{14mu} 16} \right)\end{matrix}$

In such a case, W may represent a sum of weights associated with sourcenodes i of RPR network 100 (FIG. 1), and τ may represent an upper boundof such a round trip delay τ_(i) between a bottleneck link 108 (FIG. 1)associated with a downstream node 106B of RPR network 100 (FIG. 1) andan upstream node 106A (FIG. 1) of RPR network 100 (FIG. 1), for example.Accordingly, a determination of a fair rate, as discussed below, may bebased at least in part on a round trip delay τ_(i) between a bottlenecklink 108 (FIG. 1) of RPR network 100 (FIG. 1) and at least one of sourcenodes i of RPR network 100 (FIG. 1).

A discrete implementation of the PI-type controller may be formed so asto take into consideration the occurrence of sampling at non-continuoustimes. Such a implementation of the PI-type controller in discrete timemay be based at least in part on a derivative of (eq. 7) in the realtime domain and may be expressed as follows:

F(n)=F(n−1)+K _(p)(e(n)−e(n−1))+K _(I) Te(n).   (eq. 17)

In such a case, F(n) may represent a current fair rate, n may representa sample time, F(n−1) may represent a prior fair rate, K_(p) mayrepresent a proportional gain, K_(I) may represent an integral gain,e(n) may represent a difference between the target queue length and acurrent transit queue length, e(n−1) may represent a prior differencebetween the target queue length and a current transit queue length, andT may represent a sampling time between fair rate F(n) and prior fairrate F(n−1). Accordingly, a determination of a fair rate F(n) may bebased at least in part on a difference between the target queue lengthand a current transit queue length. Additionally or alternatively, adetermination of a fair rate F(n) may be based at least in part on rateof change of a difference between the target queue length and a currenttransit queue length.

FIG. 5 illustrates a diagram of an example unbalanced traffic scenario500 arranged in accordance with the present disclosure. A PI-typecontroller 222, as described in FIGS. 2-4 may be shown to stabilizetransit queue length 402 at target queue length 404 under unbalancedtraffic scenarios. Similarly, PI-type controller 222 may be shown tostabilize an end-to-end delay of data traffic. As used herein the term“end-to-end delay” may refer to the time needed for the data from asource to reach a destination. For example, “end-to-end delay” may referto the time needed for the data from the outlet traffic 238 (FIG. 2)source associated with an upstream node to reach the egress traffic 234(FIG. 2) destination associated with a downstream node. As used hereinthe term “unbalanced traffic scenarios” may include scenarios wherethere is a variation among rates of information from upstream nodes106A, etc. For example, unbalanced traffic scenarios may includescenarios where one or more rates of information from upstream nodes106A, etc. are greedy while one or more rates of information fromupstream nodes 106A, etc. are not greedy, such as by having a givenpredetermined rate, for example.

In the example unbalanced traffic scenario 500, flow from a first node502 to a third node 506 may be greedy while a flow from a second node504 to third node 506 may be at a low rate. For example, flow fromsecond node 504 to third node 506 may be at a low rate of 50 megabitsper second (Mbps). A link 508 between first node 502 and second node 504as well as a link 510 between second node 504 and third node 506 mayhave fixed capacity, such as 622 Mbps. In unbalanced traffic scenario500, second node 504 may become congested in instances where a sum ofthe rate of flow 512 from second node 504 to third node 506 and the rateof flow 514 from first node 502 to third node 506 is greater than thelink 510 capacity between second node 504 and third node 506. In such acase, link 510 may be a bottleneck link and second node 504 maybroadcast an updated fair rate to upstream nodes, such as first node502. In the example unbalanced traffic scenario 500, forward delay τ_(i)^(f) may represent an amount of time a packet takes to go from firstnode 502 to STQ 216 (FIG. 2) of second node 504, while backward delayτ_(i) ^(b) may represent an amount of time between initiation ofcommunication of an updated fair rate at second node 504 and receipt atfirst node 502.

FIG. 6 illustrates a diagram of an example unbalanced traffic scenario600 arranged in accordance with the present disclosure. In this exampleunbalanced traffic scenario 600, there are ten nodes 601-610. Inunbalanced traffic scenario 600, all of the links 612 have the samecapacity, such as 622 Mbps, and each link 612 has a propagation delay of0.1 ms. All flows are UDP flows where all flows start at time 0. Flow614, flow 616, flow 618, and flow are greedy, and flow 622 has a rateequal to 50 Mbps. In unbalanced traffic scenario 600, unbalance trafficmay occur at link 624. Without use of PI-type controller 222 (FIG. 2)there may be oscillation during operation due to the unbalanced trafficat link 624. Such oscillation may result in a bandwidth loss. Moreover,without use of PI-type controller 222 (FIG. 2), due to the congestion,the lengths of several transient queues associated with nodes 601-610may be increased. Lastly, such oscillations may increase an end-to-enddelay and may prevent stabilization of end-to-end delay. In some cases,variation in end-to-end delay may be referred to as “delay jitter,” suchas a standard deviation of such an end-to-end delay, for example.

FIG. 7 illustrates a chart 700 of throughput over time under an exampleunbalanced traffic scenario 500, in accordance with the presentdisclosure. As illustrated, flows 512 and 514 may converge to theirrespective stabilized optimal fair rates. As used herein the term“stabilized” and/or the like may refer to being at a condition withlittle or no oscillation at the steady state.

FIG. 8 illustrates a chart 800 of throughput over time under an exampleunbalanced traffic scenario 600, in accordance with the presentdisclosure. In the simulation results illustrated in FIGS. 8-10, themeasurement time interval was set to T=1 ms, the STQ size was 256 KB,and the target length of the transit queue was set to

$q_{T} = {\frac{{STQ} - {size}}{16}.}$

The simulation results illustrated in FIGS. 8-10 were obtained by usingan RPR simulator as described in S. Gjessing, “The Simula RPR Simulatorimplemented in Java,” Simula Research Laboratory Technical Report2003-12, December 2003. As illustrated in FIG. 8, flows 614-620 and flow622 may converge to their respective stabilized optimal fair rates atthe steady state.

FIG. 9 illustrates a chart 900 of transit queue buffer occupancy overtime under an example unbalanced traffic scenario 600 in accordance withthe present disclosure. As illustrated, the transit queue bufferoccupancies associated with nodes 600-603 and node 604 stabilize. Forexample, the transit queue buffer occupancy associated with congestednode 604 may stabilize at the target value, while the transit queuebuffer occupancies associated with non-congested nodes 600-603 maystabilize near zero.

FIG. 10 illustrates a chart 1000 of end-to-end delay over time under anexample unbalanced traffic scenario 600 in accordance with the presentdisclosure. As illustrated, flow 614, flow 616, flow 618, flow 620, andflow 622 may converge to minimum end-to-end delay.

FIG. 11 illustrates an example computer program product 1100 that isarranged in accordance with the present disclosure. Program product 1100may include a signal bearing medium 1102. Signal bearing medium 1102 mayinclude one or more machine-readable instructions 1104, which, ifexecuted by one or more processors, may operatively enable a computingdevice to provide the functionality described above with respect to FIG.3 and/or FIG. 4. Thus, for example, referring to the system of FIG. 2,PI-type controller 222 may undertake one or more of the actions shown inFIG. 3 and/or FIG. 4 in response to instructions 1104 conveyed by medium1102.

In some implementations, signal bearing medium 1102 may encompass acomputer-readable medium 1106, such as, but not limited to, a hard diskdrive, a Compact Disc (CD), a Digital Video Disk (DVD), a digital tape,memory, etc. In some implementations, signal bearing medium 1102 mayencompass a recordable medium 1108, such as, but not limited to, memory,read/write (R/W) CDs, R/W DVDs, etc. In some implementations, signalbearing medium 1102 may encompass a communications medium 1110, such as,but not limited to, a digital and/or an analog communication medium(e.g., a fiber optic cable, a waveguide, a wired communications link, awireless communication link, etc.).

FIG. 12 is a block diagram illustrating an example computing device 1200that is arranged in accordance with the present disclosure. In oneexample configuration 1201, computing device 1200 may include one ormore processors 1210 and system memory 1220. A memory bus 1230 may beused for communicating between the processor 1210 and the system memory1220.

Depending on the desired configuration, processor 1210 may be of anytype including but not limited to a microprocessor (μP), amicrocontroller (μC), a digital signal processor (DSP), or anycombination thereof. Processor 1210 may include one or more levels ofcaching, such as a level one cache 1211 and a level two cache 1212, aprocessor core 1213, and registers 1214. The processor core 1213 mayinclude an arithmetic logic unit (ALU), a floating point unit (FPU), adigital signal processing core (DSP Core), or any combination thereof. Amemory controller 1215 may also be used with the processor 1210, or insome implementations the memory controller 1215 may be an internal partof the processor 1210.

Depending on the desired configuration, the system memory 1220 may be ofany type including but not limited to volatile memory (such as RAM),non-volatile memory (such as ROM, flash memory, etc.) or any combinationthereof. System memory 1220 may include an operating system 1221, one ormore applications 1222, and program data 1224. Application 1222 mayinclude an allocation of bandwidth algorithm 1223 in a resilient packetring network that is arranged to perform the functions as describedherein including the functional blocks and/or actions described withrespect to process 300 of FIG. 3 and/or process 400 of FIG. 4. ProgramData 1224 may include data 1225 for use in allocation of bandwidthalgorithm 1223, for example, data corresponding to an indication of oneor more transit queue lengths. In some example embodiments, application1222 may be arranged to operate with program data 1224 on an operatingsystem 1221 such that implementations of allocation of bandwidth may beprovided as described herein. For example, RPR node 106B may compriseall or a portion of computing device 1200 and be capable of performingall or a portion of application 1222 such that implementations ofallocation of bandwidth may be provided as described herein. Thisdescribed basic configuration is illustrated in FIG. 12 by thosecomponents within dashed line 1201.

Computing device 1200 may have additional features or functionality, andadditional interfaces to facilitate communications between the basicconfiguration 1201 and any required devices and interfaces. For example,a bus/interface controller 1240 may be used to facilitate communicationsbetween the basic configuration 1201 and one or more data storagedevices 1250 via a storage interface bus 1241. The data storage devices1250 may be removable storage devices 1251, non-removable storagedevices 1252, or a combination thereof. Examples of removable storageand non-removable storage devices include magnetic disk devices such asflexible disk drives and hard-disk drives (HDD), optical disk drivessuch as compact disk (CD) drives or digital versatile disk (DVD) drives,solid state drives (SSD), and tape drives to name a few. Examplecomputer storage media may include volatile and nonvolatile, removableand non-removable media implemented in any method or technology forstorage of information, such as computer readable instructions, datastructures, program modules, or other data.

System memory 1220, removable storage 1251 and non-removable storage1252 are all examples of computer storage media. Computer storage mediaincludes, but is not limited to, RAM, ROM, EEPROM, flash memory or othermemory technology, CD-ROM, digital versatile disks (DVD) or otheroptical storage, magnetic cassettes, magnetic tape, magnetic diskstorage or other magnetic storage devices, or any other medium which maybe used to store the desired information and which may be accessed bycomputing device 1200. Any such computer storage media may be part ofdevice 1200.

Computing device 1200 may also include an interface bus 1242 forfacilitating communication from various interface devices (e.g., outputinterfaces, peripheral interfaces, and communication interfaces) to thebasic configuration 1201 via the bus/interface controller 1240. Exampleoutput interfaces 1260 may include a graphics processing unit 1261 andan audio processing unit 1262, which may be configured to communicate tovarious external devices such as a display or speakers via one or moreA/V ports 1263. Example peripheral interfaces 1260 may include a serialinterface controller 1271 or a parallel interface controller 1272, whichmay be configured to communicate with external devices such as inputdevices (e.g., keyboard, mouse, pen, voice input device, touch inputdevice, etc.) or other peripheral devices (e.g., printer, scanner, etc.)via one or more I/O ports 1273. An example communication interface 1280includes a network controller 1281, which may be arranged to facilitatecommunications with one or more other computing devices 1290 over anetwork communication via one or more communication ports 1282. Acommunication connection is one example of a communication media.Communication media may typically be embodied by computer readableinstructions, data structures, program modules, or other data in amodulated data signal, such as a carrier wave or other transportmechanism, and may include any information delivery media. A “modulateddata signal” may be a signal that has one or more of its characteristicsset or changed in such a manner as to encode information in the signal.By way of example, and not limitation, communication media may includewired media such as a wired network or direct-wired connection, andwireless media such as acoustic, radio frequency (RF), infrared (IR) andother wireless media. The term computer readable media as used hereinmay include both storage media and communication media.

Computing device 1200 may be implemented as a portion of a small-formfactor portable (or mobile) electronic device such as a cell phone, apersonal data assistant (PDA), a personal media player device, awireless web-watch device, a personal headset device, an applicationspecific device, or a hybrid device that includes any of the abovefunctions. Computing device 1200 may also be implemented as a personalcomputer including both laptop computer and non-laptop computerconfigurations. In addition, computing device 1200 may be implemented aspart of a wireless base station or other wireless system or device suchas node 106B described above with respect to FIG. 2.

Some portions of the foregoing detailed description are presented interms of algorithms or symbolic representations of operations on databits or binary digital signals stored within a computing system memory,such as a computer memory. These algorithmic descriptions orrepresentations are examples of techniques used by those of ordinaryskill in the data processing arts to convey the substance of their workto others skilled in the art. An algorithm is here, and generally, isconsidered to be a self-consistent sequence of operations or similarprocessing leading to a desired result. In this context, operations orprocessing involve physical manipulation of physical quantities.Typically, although not necessarily, such quantities may take the formof electrical or magnetic signals capable of being stored, transferred,combined, compared or otherwise manipulated. It has proven convenient attimes, principally for reasons of common usage, to refer to such signalsas bits, data, values, elements, symbols, characters, terms, numbers,numerals or the like. It should be understood, however, that all ofthese and similar terms are to be associated with appropriate physicalquantities and are merely convenient labels. Unless specifically statedotherwise, as apparent from the following discussion, it is appreciatedthat throughout this specification discussions utilizing terms such as“processing,” “computing,” “calculating,” “determining” or the likerefer to actions or processes of a computing device, that manipulates ortransforms data represented as physical electronic or magneticquantities within memories, registers, or other information storagedevices, transmission devices, or display devices of the computingdevice.

Claimed subject matter is not limited in scope to the particularimplementations described herein. For example, some implementations maybe in hardware, such as employed to operate on a device or combinationof devices, for example, whereas other implementations may be insoftware and/or firmware. Likewise, although claimed subject matter isnot limited in scope in this respect, some implementations may includeone or more articles, such as a signal bearing medium, a storage mediumand/or storage media. This storage media, such as CD-ROMs, computerdisks, flash memory, or the like, for example, may have instructionsstored thereon, that, when executed by a computing device, such as acomputing system, computing platform, or other system, for example, mayresult in execution of a processor in accordance with claimed subjectmatter, such as one of the implementations previously described, forexample. As one possibility, a computing device may include one or moreprocessing units or processors, one or more input/output devices, suchas a display, a keyboard and/or a mouse, and one or more memories, suchas static random access memory, dynamic random access memory, flashmemory, and/or a hard drive.

There is little distinction left between hardware and softwareimplementations of aspects of systems; the use of hardware or softwareis generally (but not always, in that in certain contexts the choicebetween hardware and software may become significant) a design choicerepresenting cost vs. efficiency tradeoffs. There are various vehiclesby which processes and/or systems and/or other technologies describedherein can be effected (e.g., hardware, software, and/or firmware), andthat the preferred vehicle will vary with the context in which theprocesses and/or systems and/or other technologies are deployed. Forexample, if an implementer determines that speed and accuracy areparamount, the implementer may opt for a mainly hardware and/or firmwarevehicle; if flexibility is paramount, the implementer may opt for amainly software implementation; or, yet again alternatively, theimplementer may opt for some combination of hardware, software, and/orfirmware.

The foregoing detailed description has set forth various embodiments ofthe devices and/or processes via the use of block diagrams, flowcharts,and/or examples. Insofar as such block diagrams, flowcharts, and/orexamples contain one or more functions and/or operations, it will beunderstood by those within the art that each function and/or operationwithin such block diagrams, flowcharts, or examples can be implemented,individually and/or collectively, by a wide range of hardware, software,firmware, or virtually any combination thereof. In one embodiment,several portions of the subject matter described herein may beimplemented via Application Specific Integrated Circuits (ASICs), FieldProgrammable Gate Arrays (FPGAs), digital signal processors (DSPs), orother integrated formats. However, those skilled in the art willrecognize that some aspects of the embodiments disclosed herein, inwhole or in part, can be equivalently implemented in integratedcircuits, as one or more computer programs running on one or morecomputers (e.g., as one or more programs running on one or more computersystems), as one or more programs running on one or more processors(e.g., as one or more programs running on one or more microprocessors),as firmware, or as virtually any combination thereof, and that designingthe circuitry and/or writing the code for the software and or firmwarewould be well within the skill of one of skill in the art in light ofthis disclosure. In addition, those skilled in the art will appreciatethat the mechanisms of the subject matter described herein are capableof being distributed as a program product in a variety of forms, andthat an illustrative embodiment of the subject matter described hereinapplies regardless of the particular type of signal bearing medium usedto actually carry out the distribution. Examples of a signal bearingmedium include, but are not limited to, the following: a recordable typemedium such as a flexible disk, a hard disk drive (HDD), a Compact Disc(CD), a Digital Video Disk (DVD), a digital tape, a computer memory,etc.; and a transmission type medium such as a digital and/or an analogcommunication medium (e.g., a fiber optic cable, a waveguide, a wiredcommunications link, a wireless communication link, etc.).

Those skilled in the art will recognize that it is common within the artto describe devices and/or processes in the fashion set forth herein,and thereafter use engineering practices to integrate such describeddevices and/or processes into data processing systems. That is, at leasta portion of the devices and/or processes described herein can beintegrated into a data processing system via a reasonable amount ofexperimentation. Those having skill in the art will recognize that atypical data processing system generally includes one or more of asystem unit housing, a video display device, a memory such as volatileand non-volatile memory, processors such as microprocessors and digitalsignal processors, computational entities such as operating systems,drivers, graphical user interfaces, and applications programs, one ormore interaction devices, such as a touch pad or screen, and/or controlsystems including feedback loops and control motors (e.g., feedback forsensing position and/or velocity; control motors for moving and/oradjusting components and/or quantities). A typical data processingsystem may be implemented utilizing any suitable commercially availablecomponents, such as those typically found in datacomputing/communication and/or network computing/communication systems.

The herein described subject matter sometimes illustrates differentcomponents contained within, or connected with, different othercomponents. It is to be understood that such depicted architectures aremerely exemplary, and that in fact many other architectures can beimplemented which achieve the same functionality. In a conceptual sense,any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality can be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermedial components. Likewise, any two components soassociated can also be viewed as being “operably connected”, or“operably coupled”, to each other to achieve the desired functionality,and any two components capable of being so associated can also be viewedas being “operably couplable”, to each other to achieve the desiredfunctionality. Specific examples of operably couplable include but arenot limited to physically mateable and/or physically interactingcomponents and/or wirelessly interactable and/or wirelessly interactingcomponents and/or logically interacting and/or logically interactablecomponents.

With respect to the use of substantially any plural and/or singularterms herein, those having skill in the art can translate from theplural to the singular and/or from the singular to the plural as isappropriate to the context and/or application. The varioussingular/plural permutations may be expressly set forth herein for sakeof clarity.

It will be understood by those within the art that, in general, termsused herein, and especially in the appended claims (e.g., bodies of theappended claims) are generally intended as “open” terms (e.g., the term“including” should be interpreted as “including but not limited to,” theterm “having” should be interpreted as “having at least,” the term“includes” should be interpreted as “includes but is not limited to,”etc.). It will be further understood by those within the art that if aspecific number of an introduced claim recitation is intended, such anintent will be explicitly recited in the claim, and in the absence ofsuch recitation no such intent is present. For example, as an aid tounderstanding, the following appended claims may contain usage of theintroductory phrases “at least one” and “one or more” to introduce claimrecitations. However, the use of such phrases should not be construed toimply that the introduction of a claim recitation by the indefinitearticles “a” or “an” limits any particular claim containing suchintroduced claim recitation to inventions containing only one suchrecitation, even when the same claim includes the introductory phrases“one or more” or “at least one” and indefinite articles such as “a” or“an” (e.g., “a” and/or “an” should typically be interpreted to mean “atleast one” or “one or more”); the same holds true for the use ofdefinite articles used to introduce claim recitations. In addition, evenif a specific number of an introduced claim recitation is explicitlyrecited, those skilled in the art will recognize that such recitationshould typically be interpreted to mean at least the recited number(e.g., the bare recitation of “two recitations,” without othermodifiers, typically means at least two recitations, or two or morerecitations). Furthermore, in those instances where a conventionanalogous to “at least one of A, B, and C, etc.” is used, in generalsuch a construction is intended in the sense one having skill in the artwould understand the convention (e.g., “a system having at least one ofA, B, and C” would include but not be limited to systems that have Aalone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). In those instances where aconvention analogous to “at least one of A, B, or C, etc.” is used, ingeneral such a construction is intended in the sense one having skill inthe art would understand the convention (e.g., “a system having at leastone of A, B, or C” would include but not be limited to systems that haveA alone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). It will be furtherunderstood by those within the art that virtually any disjunctive wordand/or phrase presenting two or more alternative terms, whether in thedescription, claims, or drawings, should be understood to contemplatethe possibilities of including one of the terms, either of the terms, orboth terms. For example, the phrase “A or B” will be understood toinclude the possibilities of “A” or “B” or “A and B.”

It should also be understood that, the term “optimize” may includemaximization and/or minimization. The term “minimization” and/or thelike as used herein may include a global minimum, a local minimum, anapproximate global minimum, and/or an approximate local minimum.Likewise, it should also be understood that, the term “maximization”and/or the like as used herein may include a global maximum, a localmaximum, an approximate global maximum, and/or an approximate localmaximum.

Reference in the specification to “an implementation,” “oneimplementation,” “some implementations,” or “other implementations” maymean that a particular feature, structure, or characteristic describedin connection with one or more implementations may be included in atleast some implementations, but not necessarily in all implementations.The various appearances of “an implementation,” “one implementation,” or“some implementations” in the preceding description are not necessarilyall referring to the same implementations.

While certain exemplary techniques have been described and shown hereinusing various methods and systems, it should be understood by thoseskilled in the art that various other modifications may be made, andequivalents may be substituted, without departing from claimed subjectmatter. Additionally, many modifications may be made to adapt aparticular situation to the teachings of claimed subject matter withoutdeparting from the central concept described herein. Therefore, it isintended that claimed subject matter not be limited to the particularexamples disclosed, but that such claimed subject matter also mayinclude all implementations falling within the scope of the appendedclaims, and equivalents thereof.

1. A method implemented in a resilient packet ring network, comprising:determining a fair rate to facilitate an allocated bandwidth in theresilient packet ring network via a PI-type controller associated withat least one node of the resilient packet ring network; and stabilizingone or more transit queue lengths at a target queue length underunbalanced traffic scenarios, based at least in part on the allocatedbandwidth.
 2. The method of claim 1, wherein determining the fair ratecomprises determining a difference between the target queue length and acurrent transit queue length.
 3. The method of claim 1, whereindetermining the fair rate comprises determining a rate of change of adifference between the target queue length and a current transit queuelength.
 4. The method of claim 1, wherein determining the fair rate isbased at least in part on a round trip delay between a bottleneck linkof the resilient packet ring network and the at least one node of theresilient packet ring network.
 5. The method of claim 1, furthercomprising stabilizing an end-to-end delay associated with one or moretransit queues under unbalanced traffic scenarios, based at least inpart on the allocated bandwidth.
 6. The method of claim 1, whereindetermining the fair rate is based at least in part on a proportionalgain k_(p) expressed as: $0 < k_{p} < \frac{1}{W\; \tau}$ where W is asum of weights associated with nodes of the resilient packet ringnetwork and where τ is based at least in part on a round trip delaybetween a bottleneck link of the resilient packet ring network and theat least one node of the resilient packet ring network.
 7. The method ofclaim 1, wherein determining the fair rate is based at least in part onan integral gain k_(I) expressed as: $0 < k_{I} < \frac{k_{p}}{\tau}$where k_(p) is a proportional gain and where τ is based at least in parton a round trip delay between a bottleneck link of the resilient packetring network and the at least one node of the resilient packet ringnetwork.
 8. The method of claim 1, wherein the fair rate F(n) isexpressed as:F(n)=F(n−1)+K _(p)(e(n)−e(n−1))+K _(I) Te(n). where F(n−1) is a priorfair rate, where K_(p) is a proportional gain, where K_(I) is anintegral gain, where e(n) is a difference between the target queuelength and a current transit queue length, where e(n−1) is a priordifference between the target queue length and a current transit queuelength, and where T is a sampling time between fair rate F(n) and priorfair rate F(n−1).
 9. The method of claim 1, wherein the fair rate F(n)is expressed as:F(n)=F(n−1)+K _(p)(e(n)−e(n−1))+K _(I) Te(n). where F(n−1) is a priorfair rate, where K_(p) is a proportional gain, where K_(I) is anintegral gain, where e(n) is a difference between the target queuelength and a current transit queue length, where e(n−1) is a priordifference between the target queue length and a current transit queuelength, and where T is a sampling time between fair rate F(n) and priorfair rate F(n−1); wherein the proportional gain k_(p) is expressed as:$0 < k_{p} < \frac{1}{W\; \tau}$ where W is a sum of weightsassociated with nodes of the resilient packet ring network and where τis based at least in part on a round trip delay between a bottlenecklink of the resilient packet ring network and the at least one node ofthe resilient packet ring network; and wherein the integral gain k_(I)is expressed as: $0 < k_{I} < {\frac{k_{p}}{\tau}.}$
 10. An article foruse with a resilient packet network, comprising: a signal bearing mediumcomprising machine-readable instructions stored thereon, which, ifexecuted by one or more processors, operatively enable a computingdevice to: determine a fair rate to facilitate an allocated bandwidth inthe resilient packet ring network via a PI-type controller associatedwith at least one node of the resilient packet ring network; andstabilize one or more transit queue lengths at a target queue lengthunder unbalanced traffic scenarios, based at least in part on theallocated bandwidth.
 11. The article of claim 10, wherein thedetermination of a fair rate is based at least in part on rate of changeof a difference between the target queue length and a current transitqueue length.
 12. The article of claim 10, wherein the determination ofa fair rate is based at least in part on a round trip delay between abottleneck link of the resilient packet ring network and the at leastone node of the resilient packet ring network.
 13. The article of claim10, further comprising stabilizing an end-to-end delay associated withone or more transit queues under unbalanced traffic scenarios, based atleast in part on the allocated bandwidth.
 14. The article of claim 10,wherein the determination of a fair rate is based at least in part on aproportional gain k_(p) expressed as: $0 < k_{p} < \frac{1}{W\; \tau}$where W is a sum of weights associated with nodes of the resilientpacket ring network and where τ is based at least in part on a roundtrip delay between a bottleneck link of the resilient packet ringnetwork and the at least one node of the resilient packet ring network.15. The article of claim 10, wherein the determination of a fair rate isbased at least in part on an integral gain k_(I) expressed as:$0 < k_{I} < \frac{k_{p}}{\tau}$ where k_(p) is a proportional gain andwhere τ is based at least in part on a round trip delay between abottleneck link of the resilient packet ring network and the at leastone node of the resilient packet ring network.
 16. The article of claim10, wherein the fair rate F(n) is expressed as:F(n)=F(n−1)+K _(p)(e(n)−e(n−1))+K _(I) Te(n). where F(n−1) is a priorfair rate, where K_(p) is a proportional gain, where K_(I) is anintegral gain, where e(n) is a difference between the target queuelength and a current transit queue length, where e(n−1) is a priordifference between the target queue length and a current transit queuelength, and where T is a sampling time between fair rate F(n) and priorfair rate F(n−1).
 17. A resilient packet ring network, comprising: aplurality of nodes; an inner ring of links associated between theplurality of nodes; an outer ring of links associated between theplurality of nodes; and a PI-type controller associated with at leastone of the plurality of nodes, wherein the PI-type controller isconfigured to: determine a fair rate to facilitate an allocatedbandwidth in the resilient packet ring network, and stabilize one ormore transit queue lengths at a target queue length under unbalancedtraffic scenarios, based at least in part on the allocated bandwidth.18. The resilient packet ring network of claim 17, wherein thedetermination of a fair rate is based at least in part on a proportionalgain k_(p) expressed as: $0 < k_{p} < \frac{1}{W\; \tau}$ where W is asum of weights associated with nodes of the resilient packet ringnetwork and where τ is based at least in part on a round trip delaybetween a bottleneck link of the resilient packet ring network and theat least one node of the resilient packet ring network.
 19. Theresilient packet ring network of claim 17, wherein the determination ofa fair rate is based at least in part on an integral gain k_(I)expressed as: $0 < k_{I} < \frac{k_{p}}{\tau}$ where k_(p) is aproportional gain and where τ is based at least in part on a round tripdelay between a bottleneck link of the resilient packet ring network andthe at least one node of the resilient packet ring network.
 20. Theresilient packet ring network of claim 17, wherein the fair rate F(n) isexpressed as:F(n)=F(n−1)+K _(p)(e(n)−e(n−1))+K _(I) Te(n). where F(n−1) is a priorfair rate, where K_(p) is a proportional gain, where K_(I) is anintegral gain, where e(n) is a difference between the target queuelength and a current transit queue length, where e(n−1) is a priordifference between the target queue length and a current transit queuelength, and where T is a sampling time between fair rate F(n) and priorfair rate F(n−1).
 21. An apparatus for use with a resilient packetnetwork, comprising: a PI-type controller associated with at least oneof a plurality of nodes in the resilient packet ring network, whereinthe PI-type controller is configured to: determine a fair rate tofacilitate an allocated bandwidth in the resilient packet ring network;and stabilize one or more transit queue lengths at a target queue lengthunder unbalanced traffic scenarios, based at least in part on theallocated bandwidth.
 22. The apparatus of claim 21, wherein the PI-typecontroller is further configured to determine the fair rate based atleast in part on a proportional gain k_(p) expressed as:$0 < k_{p} < \frac{1}{W\; \tau}$ where W is a sum of weightsassociated with nodes of the resilient packet ring network and where τis based at least in part on a round trip delay between a bottlenecklink of the resilient packet ring network and the at least one node ofthe resilient packet ring network.
 23. The apparatus of claim 21,wherein the PI-type controller is further configured to determine thefair rate based at least in part on an integral gain k_(I) expressed as:$0 < k_{I} < \frac{k_{p}}{\tau}$ where k_(p) is a proportional gain andwhere τ is based at least in part on a round trip delay between abottleneck link of the resilient packet ring network and the at leastone node of the resilient packet ring network.
 24. The apparatus ofclaim 21, wherein the fair rate F(n) is expressed as:F(n)=F(n−1)+K _(p)(e(n)−e(n−1))+K _(I) Te(n). where F(n−1) is a priorfair rate, where K_(p) is a proportional gain, where K_(I) is anintegral gain, where e(n) is a difference between the target queuelength and a current transit queue length, where e(n−1) is a priordifference between the target queue length and a current transit queuelength, and where T is a sampling time between fair rate F(n) and priorfair rate F(n−1).